Strong tracking cubature Kalman filter algorithm for GPS/INS Integrated Navigation System

The Extended Kalman Filter (EKF) has been the state of the art in integrated navigation systems and especially in Pedestrian Dead-Reckoning PDR for foot-mounted Inertial Measurements Units. However in most related work with PDR, indirect filtering approach is used based on linear error Kalman Filter (KF). In this work, it is proposed to outperform this approach by the use of Direct filtering approach, which involves the non-linearity in the propagation of the orientation, velocity and in some models, in position coordinates, where the EKF can not achieve optimal estimation. We propose then, the usage of the most recent algorithms developed in the last decade; Sigma Point Kalman Filters (SPKF), especially based on Cubature rule, called Cubature Kalman Filter (CKF) as the integration algorithm for the inertial measurements. The CKF improves the mean and covariance propagation consequently comparing with EKF and previous SPKF (UKF, CDKF). Although the CKF provides a better estimate of the orientation, velocity and position with Zero velocity UPdaTes (ZUPT) measurements and Zero Angular Rate UpdaTes (ZARUT), additional sensors are necessary to measure other states such as yaw angle and to estimate properly the gyroscope bias. We studied then the possibility to integrate electronic compass as additional measure and also Map street data base or Map building data base depending on the type of navigation "Indoor", "Outdoor". In order to get much better estimation based on the Cubature rule, it is proposed to synthesize CKF in order to get robust estimation against nonlinearity of the process and the multiple measurement sensors.

Performance evaluation of Cubature Kalman filter in a GPS/IMU tightly-coupled navigation system

The extended Kalman filter (EKF) has been used widely in Global Position System (GPS) and Strapdown Inertial Navigation Systems (SINS) integrated navigation systems,which simply linearizes all nonlinear models.However, careful treatment of the nonlinearity of the system models is particularly critical when the integrated systems use low cost micro-electro-mechanical (MEMS) inertial sensors. Hence application of the EKF in MEMS inertial sensor-based integrated navigation systems will likely lead to inaccurate results. To overcome the shortcomings of the EKF, the unscented Kalman filter (UKF) has been proposed.The UKF does not require the linearization of the system models. Alternatively it uses a set of deterministically selected "sigma-points",which completely capture the true mean and covariance of the original random vector. Then these sigma-points are propagated through the nonlinear models.This captures the mean and covariance to second order accuracy for arbitrary nonlinear functions. In this paper the EKF and UKF are applied in GPS/SINS integrated systems respectively. Simulation result demonstrates that the performance of the UKF is better than the EKF in MEMS inertial sensor-based SINS/GPS integrated systems.

For land-based navigation, Euler angles are often used in INS/GPS integrated navigation systems. However, the trigonometric operations required in the updates and forming of the rotation matrices for transforming the INS measurements from the body frame to the navigation frame turns the system model to be highly nonlinear. Besides, using low-cost MEMS-based IMUs, the gyroscope bias errors must be correctly estimated and compensated, which makes the nonlinearity problem a critical one. In this contribution, three Kalman filtering methods (i.e., Extended Kalman filter with simplified system model, Extended Kalman filter with linearized system model and Unscented Kalman filter with nonlinear system model) are utilized in INS/GPS tightly-coupled integration. Simulations and field experiments are conducted. Numerical results are compared in terms of both estimation accuracy and processing time.

Object-Oriented Environment for Assessing Tracking Algorithms

Aiming at the integrated navigation system with model errors, the model errors is assumed as a process noise for Gaussian white noise to process in Kalman filtering, thus causing larger state estimation error of nonlinear filtering system and even divergent. This paper presents a nonlinear model predictive particle filtering method considers the model error of real-time estimation, and then corrects the nonlinear and non-Gaussian system model with model error. Compared and simulated the new method with the predictive filtering and the particle filtering in Strap-down Inertial Navigation System/Synthetic Aperture Radar integrated navigation system. Experiment and comparison results demonstrate that the proposed method can improve the filter performance and integrated navigation calculation accuracy significantly.

A new nonlinear filter is derived for continuous-time processes with discrete-time measurements. The filter is exact, and it can be implemented in real time with a computational complexity that is comparable to the Kalman filter. This new filter includes both the Kalman filter and the discrete-time version of the Benes filter as special cases. Moreover, the new theory can handle a large class of nonlinear estimation problems that cannot be solved using the Kalman or discrete-time Benes filters. A simple approximation technique is suggested for practical applications in which the dynamics do not satisfy the required conditions exactly. This approximation is analogous to the so-called "extended Kalman filter" [10], and it represents a generalization of the standard linearization method.

The conventional Kalman filter assumes that the system model and the observation model is linearity. Also the noise in system and observation model is white noise. However the practical environment is very complex. When we use Kalman filter to estimate, we can not got the transcendent information. The paper considers the characteristic of aircraft, research the structure and scheme of INS/CNS/GPS integrated navigation system. The error model of integrated navigation system has been set up. The status of navigation system has been estimated with Kalman filter, and the simulation calculation has been progressed. The paper presents a method, which use neural network ensembles to deal with the Kalman filter. This method improves the generalization and stabilization ability. The simulation shows that the arithmetic has high precision.

Aiming at the problem of improving the navigation accuracy of ships, a Kalman filter algorithm based on optimization is proposed for navigation optimization. On the basis of studying the dead reckoning knowledge, we establish the dimensional dynamic equation of the ship integrated navigation system. Then the extended Kalman filter is adjusted by using fuzzy logic adaptive controller (FLAC) and it is applied to GPS/INS information fusion to enable it to have adaptive ability to deal with environment disturbance. Finally, the method is used to simulate the GPS/INS integrated navigation system on MATLAB platform. The results show that the improved model can effectively use part of the system data to update and iterate, and improve the stability and reliability of the filter, so it is also better suitable for ship navigation and target tracking.

A new integrated navigation system designed for small size Unmanned Aerial Vehicles (UAVs) is presented. The proposed system is based on a number of low-cost avionics sensors, including Global Navigation Satellite Systems (GNSS), Micro-Electro-Mechanical System (MEMS) based Inertial Measurement Unit (IMU) and Vision Based Sensors (VBS). The use of an Aircraft Dynamics Models (ADMs) to provide additional information to compensate for the shortcomings of Vision Based Navigation (VBN) and MEMS-IMU sensors in high-dynamics attitude determination tasks is also considered. Additionally, the research concentrates on the potential of carrier-phase GNSS for Attitude Determination (GAD) using interferometric techniques. The main objective is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance (position and attitude data) in all phases of flight of small UAVs, with a special focus on precision approach and landing, where VBN techniques can be fully exploited in a multi-sensor data fusion architecture. An Extended Kalman Filter (EKF) is developed to integrate the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UAV platform in real-time. Three different integrated navigation system architectures are implemented. The first architecture uses VBN at 20 Hz and GNSS at 1 Hz to augment the MEMS-IMU running at 100 Hz. The second mode also includes the ADM (computations performed at 100 Hz) to provide augmentation of the attitude channel. The third fusion architecture uses GNSS based attitude values. The simulations are carried out on the AEROSONDE UAV performing high-dynamics manoeuvres repre-sentative of the UAV operational flight envelope. Simulation of the VBN-IMU-GNSS (VIG) integrated navigation system shows that the system can attain position, velocity and attitude accuracies complying with Category Two (CAT II) precision approach requirements. Simulation of the VBN-IMU-GNSS-ADM (VIGA) system also shows promising results, since the achieved attitude accuracy is higher using the ADM-VBN-IMU than using VBN-IMU only. However, due to rapid divergence of the ADM virtual sensor, there is a need for frequent re-initialisation of the ADM data module, which is strongly dependent on the UAV flight dynamics and the specific manoeuvring transitions performed. In the simulation of the third integrated navigation system, the VIG system is augmented by employing the GAD, forming the VIG-GAD (VIGGA) system architecture. The performances achieved with the VIG, VIGA and VIGGA integrated Navigation and Guidance System (NGS) are presented and are in line with the International Civil Aviation Organization (ICAO) precision approach requirements.

This paper presents a new robust adaptive unscented particle filtering algorithm by adopting the concept of the adaptive robust filtering to the unscented particle filter. This algorithm adaptively determines the equivalent weight function and adaptively adjusts the adaptive factor constructed from predicted residuals to resist the disturbances of singular observations and the kinematic model noise, thus preventing particles from degeneracy. It also uses the unscented transformation to improve the accuracy of particle filtering, thus providing the reliable state estimation for improving the performance of adaptive robust filtering. Experiments and comparison analysis demonstrate that the proposed filtering algorithm can effectively resist disturbances due to system state noise and observation noise, and the filtering accuracy is much higher than the extended Kalman filter, unscented Kalman filter, standard particle filter and unscented particle filter.

This paper proposes an improved initial alignment method for a strap-down inertial navigation system/global navigation satellite system (SINS/GNSS) integrated navigation system with large misalignment angles. Its methodology is based on the three-dimensional special Euclidean group and extended Kalman filter (SE2(3)/EKF) and aims to overcome the challenges of achieving fast alignment under large misalignment angles using traditional methods. To accurately characterize the state errors of attitude, velocity, and position, these elements are constructed as elements of a Lie group. The nonlinear error on the Lie group can then be well quantified. Additionally, a group vector mixed error model is developed, taking into account the zero bias errors of gyroscopes and accelerometers. Using this new error definition, a GNSS-assisted SINS dynamic initial alignment algorithm is derived, which is based on the invariance of velocity and position measurements. Simulation experiments demonstrate that the alignment method based on SE2(3)/EKF can achieve a higher accuracy in various scenarios with large misalignment angles, while the attitude error can be rapidly reduced to a lower level.

Navigation includes the integration of methodologies and systems for estimating time-varying position, velocity and attitude of moving objects. Navigation incorporating the integrated inertial navigation system (INS) and global positioning system (GPS) generally requires extensive evaluations of nonlinear equations involving double integration. Currently, integrated navigation systems are commonly implemented using the extended Kalman filter (EKF). The EKF assumes a linearized process, measurement models and Gaussian noise distributions. These assumptions are unrealistic for highly nonlinear systems like land vehicle navigation and may cause filter divergence. A particle filter (PF) is developed to enhance integrated INS/GPS system performance as it can easily deal with nonlinearity and non-Gaussian noises. In this paper, a hybrid extended particle filter (HEPF) is developed as an alternative to the well-known EKF to achieve better navigation data accuracy for low-cost microelectromechanical system sensors. The results show that the HEPF performs better than the EKF during GPS outages, especially when simulated outages are located in periods with high vehicle dynamics.

The integration of position and velocity is commonly used for observation model in the GPS/INS integrated navigation system, but correlation between the system’s measurements of this observation model decrease the navigation accuracy. So the integration of pseudo-range was adopted for observation model to eliminate the influence of correlation. As the observation model is nonlinear, the unscented particle filter (UPF) was introduced for states estimation to eliminate the linearization error. The simulation was carried out under the condition of less than four GPS satellites data and the filtering results of UPF method were compared with the results of extended Kalman filter (EKF) method. The simulation results show that the estimated values with both UPF and EKF method are close to the real values but the estimation error of UPF algorithm is smaller than that of EKF method.

The robust adaptive filtering method based on the State Dependent Riccati Equation technique for SINS/SAR integrated navigation system. This method adopts the state dependent coefficient form to convert nonlinear system model into linear system for avoiding the errors caused by the traditional numerical linearization process. It also adopts the concepts of robust estimation and adaptive factor to construct reasonably the discriminate statistics and adaptive factor for resisting the disturbances of singular observations and kinematic model error. Experimental results and comparison analysis demonstrate that the proposed filtering method can not only effectively resist disturbances from nonlinear system state noise and observation noise, but it also can achieve higher accuracy than the extended kalman filtering and SDRE filtering methods.